Q.25Suppose that a sample of gas expands from 2.0 to 8.0 m3 along the diagonal path in the pV diagram shown in Fig. 23.33. It is then compressed back to 2.0 m3 along cither path 1 or path 2. Compute the net work done on the gas for th4 complete cycle in each case.

Combining two paths, we will get a rectangle. The diagonal of the rectangle will create two right angel triangles. So the area will be same for each path.
The area A of the rectangle is,


So the area of path 1 which is in the direction counterclockwise will be -45 J. It signifies that the work done on the gas will be – (-45 kJ) or 45 kJ. Thus the work done on the gas for path 2 will be the negative of path 1, as it is in the clockwise direction. Therefore the area for path 2 will be 45 kJ.